Cheryl Cole has been told she can return to the US version of The X Factor if she can prove her commitment. Photograph: Graham Whitby Boot/Sportsphoto/Allstar

Cheryl Cole can keep her $1.2m position as a judge on the US version of The X Factor if she can demonstrate to Simon Cowell and TV network Fox that she is committed to "making the programme work".

She has to agree to rejoin the judging panel by this Wednesday when The X Factor auditions move to New York – and perform better on screen than in earlier auditions which nearly led to her being dropped.

Cole was described as "not herself" by US television sources in the earlier US auditions, which led to Cowell and the TV network to suggest that she move back to be a judge on the original version of the X Factor.

News of those conversations began to leak a week and a half ago, but the initial speculation centred on the suggestion that she had been fired from the US show, partly because Fox executives could not understand her accent.

Cowell and Fox chose not to deny the speculation as furious behind-the scenes manoeuvres followed – and a battle broke out over what would happen to the Girls Aloud singer.

On this account, Cole first asked for £2m to appear in the X Factor UK as a consolation prize, double her previous fee. ITV balked at that figure – and Cole did not sign up. Since then Cole and her team have "gone to ground", and become hard to negotiate with.

What is less clear, though, is whether the now public wooing of Cole represents a genuine offer or part of a spin strategy to make Cowell, his team and Fox appear reasonable when they believe Cole will not participate.

Cole could also take a lesser role in the US show as an alternative to being a judge, but whatever happens she has been promised that she will receive her fee from Fox – estimated at $1.2m. There had been speculation that she would not be paid.

Friends of Cole say that she has been beset with conflicting advice during the X Factor crisis reflecting "a host of personal agendas". She has been advised to spend some time "concentrating on her musical career" in an effort to move on from the US fiasco – but is also considering a role as a judge on new singing reality show format The Voice, which is being fought over by both the BBC and ITV.

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